Verfügbarkeit: Introduction to partial differential equations

Introduction to partial differential equations:

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Bibliographische Detailangaben
Beteilige Person:	Folland, Gerald B. 1947- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Princeton, NJ Princeton Univ. Press 1995
Ausgabe:	2. ed.
Schlagwörter:	Équations aux dérivées partielles Partielle Differentialgleichung
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007948818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Hier auch später erschienene, unveränderte Nachdrucke
Umfang:	XI, 324 S.
ISBN:	0691043612 9780691043616

Internformat

MARC


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Datensatz im Suchindex

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adam_text	CONTENTS PREFACE ix Chapter 0 PRELIMINARIES 1 A. Notations and Definitions 1 B. Results from Advanced Calculus 4 C. Convolutions 9 D. The Fourier Transform 14 E. Distributions 17 F. Compact Operators 22 Chapter 1 LOCAL EXISTENCE THEORY 30 A. Basic Concepts 30 B. Real First Order Equations 34 C. The General Cauchy Problem 42 D. The Cauchy Kowalevski Theorem 46 E. Local Solvability: the Lewy Example 56 F. Constant Coefficient Operators: Fundamental Solutions 59 Chapter 2 THE LAPLACE OPERATOR 66 A. Symmetry Properties of the Laplacian 67 B. Basic Properties of Harmonic Functions 68 C. The Fundamental Solution 74 D. The Dirichlet and Neumann Problems 83 E. The Green s Function 85 F. Dirichlet s Principle 88 G. The Dirichlet Problem in a Half Space 91 H. The Dirichlet Problem in a Ball 95 I. More about Harmonic Functions 110 vi Contents Chapter 3 LAYER POTENTIALS 116 A. The Setup 116 B. Integral Operators 120 C. Double Layer Potentials 123 D. Single Layer Potentials 129 E. Solution of the Problems 134 F. Further Remarks 139 Chapter 4 THE HEAT OPERATOR 142 A. The Gaussian Kernel 143 B. Functions of the Laplacian 149 C. The Heat Equation in Bounded Domains 155 Chapter 5 THE WAVE OPERATOR 159 A. The Cauchy Problem 160 B. Solution of the Cauchy Problem 165 C. The Inhomogeneous Equation 174 D. Fourier Analysis of the Wave Operator 177 E. The Wave Equation in Bounded Domains 183 F. The Radon Transform 185 Chapter 6 THE L2 THEORY OF DERIVATIVES 190 A. Sobolev Spaces on 1 190 B. Further Results on Sobolev Spaces 200 C. Local Regularity of Elliptic Operators 210 D. Constant Coefficient Hypoelliptic Operators 215 E. Sobolev Spaces on Bounded Domains 220 Chapter 7 ELLIPTIC BOUNDARY VALUE PROBLEMS 228 A. Strong Ellipticity 228 B. On Integration by Parts 231 C. Dirichlet Forms and Boundary Conditions 237 D. The Coercive Estimate 242 E. Existence, Uniqueness, and Eigenvalues 248 F. Regularity at the Boundary: the Second Order Case 253 G. Further Results and Techniques 261 H. Epilogue: the Return of the Green s Function 263 Contents vii Chapter 8 PSEUDODIFFERENTIAL OPERATORS 266 A. Basic Definitions and Properties 266 B. Kernels of Pseudodifferential Operators 271 C. Asymptotic Expansions of Symbols 279 D. Amplitudes, Adjoints, and Products 283 E. Sobolev Estimates 295 F. Elliptic Operators 297 G. Introduction to Microlocal Analysis 304 H. Change of Coordinates 310 BIBLIOGRAPHY 317 INDEX OF SYMBOLS 320 INDEX 322
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isbn	0691043612 9780691043616
language	English
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spellingShingle	Folland, Gerald B. 1947- Introduction to partial differential equations Équations aux dérivées partielles Équations aux dérivées partielles ram Partielle Differentialgleichung (DE-588)4044779-0 gnd
subject_GND	(DE-588)4044779-0
title	Introduction to partial differential equations
title_auth	Introduction to partial differential equations
title_exact_search	Introduction to partial differential equations
title_full	Introduction to partial differential equations Gerald B. Folland
title_fullStr	Introduction to partial differential equations Gerald B. Folland
title_full_unstemmed	Introduction to partial differential equations Gerald B. Folland
title_short	Introduction to partial differential equations
title_sort	introduction to partial differential equations
topic	Équations aux dérivées partielles Équations aux dérivées partielles ram Partielle Differentialgleichung (DE-588)4044779-0 gnd
topic_facet	Équations aux dérivées partielles Partielle Differentialgleichung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007948818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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